Participants will be admitted to the NIH Clinical Center for 2 to 3 days. Stem cells will be collected either from cord blood (in newborn patients) or from the bone marrow. The bone marrow procedure is done under light sedation or general anesthesia. It involves drawing a small amount of marrow through a needle inserted into the hip bone. The stem cells in the marrow will be grown in the laboratory and a normal human ADA gene will be transferred into them through a special type of disabled mouse virus. A few days later, the patient will receive the ADA-corrected cells through an infusion in the vein that will last from 10 minutes to 2 hours.